Note that for some lightweight road bars the creaking comes from the metal sleeve that is glued over the enlarged center section of the bar. The glue softens and creaks, and there's not really much that can be done about it other than to replace the bar or wait for friction to wear away the rubbing surfaces a bit.
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Daniel R HicksSep 15 '12 at 2:47

Are you positive it's coming from the handlebar to stem interface? Creaking sounds are notoriously hard to diagnose. It's highly possible that the noise could be from the stem to steer tube interface or your headset or the spacers on your steer tube or topcap or another source, while it may sound like it's coming from your handlebars.

Also, be cautious with making things "as tight as I can make it" as you may risk over-tightening the part and risking more damage to your bike and/or components. If you are unfamiliar with how hard to tighten bolts, you should consult your owner's manual, the part manufacturers technical documents or simply take your bike into a reputable mechanic to properly tighten everything.

+1: over-tightening the handlebar clamp in particular can lead to the bar snapping at the edge of the clamp. If your stem is an aheadset with 4-bolt faceplate holding the bar, try to make sure all 4 bolts are evenly tight, so you're not focussing the pressure on one spot
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UselessSep 16 '12 at 9:32

Fair enough. I can't be certain of anything. Something seems slightly loose if I twist on the bar. It is an adjustable stem so it may also be that. I've never personally adjusted the adjustable stem. What I meant by "tight as I can make it" is that using a crappy Allen key the bolts were definitely very tight as assembled by the bike shop.
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RichardMSep 18 '12 at 19:27

From the fact that you say "Something seems slightly loose if I twist on the bar", there is also some chance that you have mismatched handlebar and stem. There are 25.4mm and 26.0mm clamp area diameters for both handlebars and stems, so you might have a 25.4mm bar in a 26.0 stem, which might make it creaky and loose. You could try removing the handlebar and sticking a Nitto or beer can shim around the clamping area of the bar and remounting it. If you can't fit the bar into the stem's clamp with the shim, then this isn't the problem.